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  <h1>Source code for torch.nn.modules.fold</h1><div class="highlight"><pre>
<span></span><span class="c1"># coding=utf-8</span>
<span class="kn">from</span> <span class="nn">.module</span> <span class="kn">import</span> <span class="n">Module</span>
<span class="kn">from</span> <span class="nn">..</span> <span class="kn">import</span> <span class="n">functional</span> <span class="k">as</span> <span class="n">F</span>


<div class="viewcode-block" id="Fold"><a class="viewcode-back" href="../../../../nn.html#torch.nn.Fold">[docs]</a><span class="k">class</span> <span class="nc">Fold</span><span class="p">(</span><span class="n">Module</span><span class="p">):</span>
    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Combines an array of sliding local blocks into a large containing</span>
<span class="sd">    tensor.</span>

<span class="sd">    Consider a batched :attr:`input` tensor containing sliding local blocks,</span>
<span class="sd">    e.g., patches of images, of shape :math:`(N, C \times  \prod(\text{kernel\_size}), L)`,</span>
<span class="sd">    where :math:`N` is batch dimension, :math:`C \times \prod(\text{kernel\_size})`</span>
<span class="sd">    is the number of values within a block (a block has :math:`\prod(\text{kernel\_size})`</span>
<span class="sd">    spatial locations each containing a :math:`C`-channeled vector), and</span>
<span class="sd">    :math:`L` is the total number of blocks. (This is exactly the</span>
<span class="sd">    same specification as the output shape of :class:`~torch.nn.Unfold`.) This</span>
<span class="sd">    operation combines these local blocks into the large :attr:`output` tensor</span>
<span class="sd">    of shape :math:`(N, C, \text{output\_size}[0], \text{output\_size}[1], \dots)`</span>
<span class="sd">    by summing the overlapping values. Similar to :class:`~torch.nn.Unfold`, the</span>
<span class="sd">    arguments must satisfy</span>

<span class="sd">    .. math::</span>
<span class="sd">        L = \prod_d \left\lfloor\frac{\text{output\_size}[d] + 2 \times \text{padding}[d] %</span>
<span class="sd">            - \text{dilation}[d] \times (\text{kernel\_size}[d] - 1) - 1}{\text{stride}[d]} + 1\right\rfloor,</span>

<span class="sd">    where :math:`d` is over all spatial dimensions.</span>

<span class="sd">    * :attr:`output_size` describes the spatial shape of the large containing</span>
<span class="sd">      tensor of the sliding local blocks. It is useful to resolve the ambiguity</span>
<span class="sd">      when multiple input shapes map to same number of sliding blocks, e.g.,</span>
<span class="sd">      with ``stride &gt; 0``.</span>

<span class="sd">    The :attr:`padding`, :attr:`stride` and :attr:`dilation` arguments specify</span>
<span class="sd">    how the sliding blocks are retrieved.</span>

<span class="sd">    * :attr:`stride` controls the stride for the sliding blocks.</span>

<span class="sd">    * :attr:`padding` controls the amount of implicit zero-paddings on both</span>
<span class="sd">      sides for :attr:`padding` number of points for each dimension before</span>
<span class="sd">      reshaping.</span>

<span class="sd">    * :attr:`dilation` controls the spacing between the kernel points; also known as the à trous algorithm.</span>
<span class="sd">      It is harder to describe, but this `link`_ has a nice visualization of what :attr:`dilation` does.</span>

<span class="sd">    Args:</span>
<span class="sd">        output_size (int or tuple): the shape of the spatial dimensions of the</span>
<span class="sd">                                    output (i.e., ``output.sizes()[2:]``)</span>
<span class="sd">        kernel_size (int or tuple): the size of the sliding blocks</span>
<span class="sd">        stride (int or tuple): the stride of the sliding blocks in the input</span>
<span class="sd">                               spatial dimensions. Default: 1</span>
<span class="sd">        padding (int or tuple, optional): implicit zero padding to be added on</span>
<span class="sd">                                          both sides of input. Default: 0</span>
<span class="sd">        dilation (int or tuple, optional): a parameter that controls the</span>
<span class="sd">                                           stride of elements within the</span>
<span class="sd">                                           neighborhood. Default: 1</span>

<span class="sd">    * If :attr:`output_size`, :attr:`kernel_size`, :attr:`dilation`,</span>
<span class="sd">      :attr:`padding` or :attr:`stride` is an int or a tuple of length 1 then</span>
<span class="sd">      their values will be replicated across all spatial dimensions.</span>

<span class="sd">    * For the case of two output spatial dimensions this operation is sometimes</span>
<span class="sd">      called ``col2im``.</span>

<span class="sd">    .. note::</span>
<span class="sd">        :class:`~torch.nn.Fold` calculates each combined value in the resulting</span>
<span class="sd">        large tensor by summing all values from all containing blocks.</span>
<span class="sd">        :class:`~torch.nn.Unfold` extracts the values in the local blocks by</span>
<span class="sd">        copying from the large tensor. So, if the blocks overlap, they are not</span>
<span class="sd">        inverses of each other.</span>

<span class="sd">        In general, folding and unfolding operations are related as</span>
<span class="sd">        follows. Consider :class:`~torch.nn.Fold` and</span>
<span class="sd">        :class:`~torch.nn.Unfold` instances created with the same</span>
<span class="sd">        parameters:</span>

<span class="sd">        &gt;&gt;&gt; fold_params = dict(kernel_size=..., dilation=..., padding=..., stride=...)</span>
<span class="sd">        &gt;&gt;&gt; fold = nn.Fold(output_size=..., **fold_params)</span>
<span class="sd">        &gt;&gt;&gt; unfold = nn.Unfold(**fold_params)</span>

<span class="sd">        Then for any (supported) ``input`` tensor the following</span>
<span class="sd">        equality holds:</span>

<span class="sd">        ::</span>

<span class="sd">            fold(unfold(input)) == divisor * input</span>

<span class="sd">        where ``divisor`` is a tensor that depends only on the shape</span>
<span class="sd">        and dtype of the ``input``:</span>

<span class="sd">        &gt;&gt;&gt; input_ones = torch.ones(input.shape, dtype=input.dtype)</span>
<span class="sd">        &gt;&gt;&gt; divisor = fold(unfold(input_ones))</span>

<span class="sd">        When the ``divisor`` tensor contains no zero elements, then</span>
<span class="sd">        ``fold`` and ``unfold`` operations are inverses of each</span>
<span class="sd">        other (up to constant divisor).</span>

<span class="sd">    .. warning::</span>
<span class="sd">        Currently, only 4-D output tensors (batched image-like tensors) are</span>
<span class="sd">        supported.</span>

<span class="sd">    Shape:</span>
<span class="sd">        - Input: :math:`(N, C \times \prod(\text{kernel\_size}), L)`</span>
<span class="sd">        - Output: :math:`(N, C, \text{output\_size}[0], \text{output\_size}[1], \dots)` as described above</span>

<span class="sd">    Examples::</span>

<span class="sd">        &gt;&gt;&gt; fold = nn.Fold(output_size=(4, 5), kernel_size=(2, 2))</span>
<span class="sd">        &gt;&gt;&gt; input = torch.randn(1, 3 * 2 * 2, 12)</span>
<span class="sd">        &gt;&gt;&gt; output = fold(input)</span>
<span class="sd">        &gt;&gt;&gt; output.size()</span>
<span class="sd">        torch.Size([1, 3, 4, 5])</span>

<span class="sd">    .. _link:</span>
<span class="sd">        https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md</span>

<span class="sd">    &quot;&quot;&quot;</span>
    <span class="n">__constants__</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;output_size&#39;</span><span class="p">,</span> <span class="s1">&#39;kernel_size&#39;</span><span class="p">,</span> <span class="s1">&#39;dilation&#39;</span><span class="p">,</span> <span class="s1">&#39;padding&#39;</span><span class="p">,</span>
                     <span class="s1">&#39;stride&#39;</span><span class="p">]</span>

    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">output_size</span><span class="p">,</span> <span class="n">kernel_size</span><span class="p">,</span> <span class="n">dilation</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">stride</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
        <span class="nb">super</span><span class="p">(</span><span class="n">Fold</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">output_size</span> <span class="o">=</span> <span class="n">output_size</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">kernel_size</span> <span class="o">=</span> <span class="n">kernel_size</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">dilation</span> <span class="o">=</span> <span class="n">dilation</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">padding</span> <span class="o">=</span> <span class="n">padding</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">stride</span> <span class="o">=</span> <span class="n">stride</span>

    <span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="nb">input</span><span class="p">):</span>
        <span class="k">return</span> <span class="n">F</span><span class="o">.</span><span class="n">fold</span><span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">output_size</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">kernel_size</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">dilation</span><span class="p">,</span>
                      <span class="bp">self</span><span class="o">.</span><span class="n">padding</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">stride</span><span class="p">)</span>

    <span class="k">def</span> <span class="nf">extra_repr</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="s1">&#39;output_size=</span><span class="si">{output_size}</span><span class="s1">, kernel_size=</span><span class="si">{kernel_size}</span><span class="s1">, &#39;</span> \
            <span class="s1">&#39;dilation=</span><span class="si">{dilation}</span><span class="s1">, padding=</span><span class="si">{padding}</span><span class="s1">, stride=</span><span class="si">{stride}</span><span class="s1">&#39;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span>
                <span class="o">**</span><span class="bp">self</span><span class="o">.</span><span class="vm">__dict__</span>
            <span class="p">)</span></div>


<div class="viewcode-block" id="Unfold"><a class="viewcode-back" href="../../../../nn.html#torch.nn.Unfold">[docs]</a><span class="k">class</span> <span class="nc">Unfold</span><span class="p">(</span><span class="n">Module</span><span class="p">):</span>
    <span class="sa">r</span><span class="sd">&quot;&quot;&quot;Extracts sliding local blocks from a batched input tensor.</span>

<span class="sd">    Consider a batched :attr:`input` tensor of shape :math:`(N, C, *)`,</span>
<span class="sd">    where :math:`N` is the batch dimension, :math:`C` is the channel dimension,</span>
<span class="sd">    and :math:`*` represent arbitrary spatial dimensions. This operation flattens</span>
<span class="sd">    each sliding :attr:`kernel_size`-sized block within the spatial dimensions</span>
<span class="sd">    of :attr:`input` into a column (i.e., last dimension) of a 3-D :attr:`output`</span>
<span class="sd">    tensor of shape :math:`(N, C \times \prod(\text{kernel\_size}), L)`, where</span>
<span class="sd">    :math:`C \times \prod(\text{kernel\_size})` is the total number of values</span>
<span class="sd">    within each block (a block has :math:`\prod(\text{kernel\_size})` spatial</span>
<span class="sd">    locations each containing a :math:`C`-channeled vector), and :math:`L` is</span>
<span class="sd">    the total number of such blocks:</span>

<span class="sd">    .. math::</span>
<span class="sd">        L = \prod_d \left\lfloor\frac{\text{spatial\_size}[d] + 2 \times \text{padding}[d] %</span>
<span class="sd">            - \text{dilation}[d] \times (\text{kernel\_size}[d] - 1) - 1}{\text{stride}[d]} + 1\right\rfloor,</span>

<span class="sd">    where :math:`\text{spatial\_size}` is formed by the spatial dimensions</span>
<span class="sd">    of :attr:`input` (:math:`*` above), and :math:`d` is over all spatial</span>
<span class="sd">    dimensions.</span>

<span class="sd">    Therefore, indexing :attr:`output` at the last dimension (column dimension)</span>
<span class="sd">    gives all values within a certain block.</span>

<span class="sd">    The :attr:`padding`, :attr:`stride` and :attr:`dilation` arguments specify</span>
<span class="sd">    how the sliding blocks are retrieved.</span>

<span class="sd">    * :attr:`stride` controls the stride for the sliding blocks.</span>

<span class="sd">    * :attr:`padding` controls the amount of implicit zero-paddings on both</span>
<span class="sd">      sides for :attr:`padding` number of points for each dimension before</span>
<span class="sd">      reshaping.</span>

<span class="sd">    * :attr:`dilation` controls the spacing between the kernel points; also known as the à trous algorithm.</span>
<span class="sd">      It is harder to describe, but this `link`_ has a nice visualization of what :attr:`dilation` does.</span>

<span class="sd">    Args:</span>
<span class="sd">        kernel_size (int or tuple): the size of the sliding blocks</span>
<span class="sd">        stride (int or tuple, optional): the stride of the sliding blocks in the input</span>
<span class="sd">                                         spatial dimensions. Default: 1</span>
<span class="sd">        padding (int or tuple, optional): implicit zero padding to be added on</span>
<span class="sd">                                          both sides of input. Default: 0</span>
<span class="sd">        dilation (int or tuple, optional): a parameter that controls the</span>
<span class="sd">                                           stride of elements within the</span>
<span class="sd">                                           neighborhood. Default: 1</span>

<span class="sd">    * If :attr:`kernel_size`, :attr:`dilation`, :attr:`padding` or</span>
<span class="sd">      :attr:`stride` is an int or a tuple of length 1, their values will be</span>
<span class="sd">      replicated across all spatial dimensions.</span>

<span class="sd">    * For the case of two input spatial dimensions this operation is sometimes</span>
<span class="sd">      called ``im2col``.</span>

<span class="sd">    .. note::</span>
<span class="sd">        :class:`~torch.nn.Fold` calculates each combined value in the resulting</span>
<span class="sd">        large tensor by summing all values from all containing blocks.</span>
<span class="sd">        :class:`~torch.nn.Unfold` extracts the values in the local blocks by</span>
<span class="sd">        copying from the large tensor. So, if the blocks overlap, they are not</span>
<span class="sd">        inverses of each other.</span>

<span class="sd">        In general, folding and unfolding operations are related as</span>
<span class="sd">        follows. Consider :class:`~torch.nn.Fold` and</span>
<span class="sd">        :class:`~torch.nn.Unfold` instances created with the same</span>
<span class="sd">        parameters:</span>

<span class="sd">        &gt;&gt;&gt; fold_params = dict(kernel_size=..., dilation=..., padding=..., stride=...)</span>
<span class="sd">        &gt;&gt;&gt; fold = nn.Fold(output_size=..., **fold_params)</span>
<span class="sd">        &gt;&gt;&gt; unfold = nn.Unfold(**fold_params)</span>

<span class="sd">        Then for any (supported) ``input`` tensor the following</span>
<span class="sd">        equality holds:</span>

<span class="sd">        ::</span>

<span class="sd">            fold(unfold(input)) == divisor * input</span>

<span class="sd">        where ``divisor`` is a tensor that depends only on the shape</span>
<span class="sd">        and dtype of the ``input``:</span>

<span class="sd">        &gt;&gt;&gt; input_ones = torch.ones(input.shape, dtype=input.dtype)</span>
<span class="sd">        &gt;&gt;&gt; divisor = fold(unfold(input_ones))</span>

<span class="sd">        When the ``divisor`` tensor contains no zero elements, then</span>
<span class="sd">        ``fold`` and ``unfold`` operations are inverses of each</span>
<span class="sd">        other (up to constant divisor).</span>

<span class="sd">    .. warning::</span>
<span class="sd">        Currently, only 4-D input tensors (batched image-like tensors) are</span>
<span class="sd">        supported.</span>

<span class="sd">    Shape:</span>
<span class="sd">        - Input: :math:`(N, C, *)`</span>
<span class="sd">        - Output: :math:`(N, C \times \prod(\text{kernel\_size}), L)` as described above</span>

<span class="sd">    Examples::</span>

<span class="sd">        &gt;&gt;&gt; unfold = nn.Unfold(kernel_size=(2, 3))</span>
<span class="sd">        &gt;&gt;&gt; input = torch.randn(2, 5, 3, 4)</span>
<span class="sd">        &gt;&gt;&gt; output = unfold(input)</span>
<span class="sd">        &gt;&gt;&gt; # each patch contains 30 values (2x3=6 vectors, each of 5 channels)</span>
<span class="sd">        &gt;&gt;&gt; # 4 blocks (2x3 kernels) in total in the 3x4 input</span>
<span class="sd">        &gt;&gt;&gt; output.size()</span>
<span class="sd">        torch.Size([2, 30, 4])</span>

<span class="sd">        &gt;&gt;&gt; # Convolution is equivalent with Unfold + Matrix Multiplication + Fold (or view to output shape)</span>
<span class="sd">        &gt;&gt;&gt; inp = torch.randn(1, 3, 10, 12)</span>
<span class="sd">        &gt;&gt;&gt; w = torch.randn(2, 3, 4, 5)</span>
<span class="sd">        &gt;&gt;&gt; inp_unf = torch.nn.functional.unfold(inp, (4, 5))</span>
<span class="sd">        &gt;&gt;&gt; out_unf = inp_unf.transpose(1, 2).matmul(w.view(w.size(0), -1).t()).transpose(1, 2)</span>
<span class="sd">        &gt;&gt;&gt; out = torch.nn.functional.fold(out_unf, (7, 8), (1, 1))</span>
<span class="sd">        &gt;&gt;&gt; # or equivalently (and avoiding a copy),</span>
<span class="sd">        &gt;&gt;&gt; # out = out_unf.view(1, 2, 7, 8)</span>
<span class="sd">        &gt;&gt;&gt; (torch.nn.functional.conv2d(inp, w) - out).abs().max()</span>
<span class="sd">        tensor(1.9073e-06)</span>

<span class="sd">    .. _link:</span>
<span class="sd">        https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md</span>

<span class="sd">    &quot;&quot;&quot;</span>
    <span class="n">__constants__</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;kernel_size&#39;</span><span class="p">,</span> <span class="s1">&#39;dilation&#39;</span><span class="p">,</span> <span class="s1">&#39;padding&#39;</span><span class="p">,</span> <span class="s1">&#39;stride&#39;</span><span class="p">]</span>

    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">kernel_size</span><span class="p">,</span> <span class="n">dilation</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">stride</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
        <span class="nb">super</span><span class="p">(</span><span class="n">Unfold</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">kernel_size</span> <span class="o">=</span> <span class="n">kernel_size</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">dilation</span> <span class="o">=</span> <span class="n">dilation</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">padding</span> <span class="o">=</span> <span class="n">padding</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">stride</span> <span class="o">=</span> <span class="n">stride</span>

    <span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="nb">input</span><span class="p">):</span>
        <span class="k">return</span> <span class="n">F</span><span class="o">.</span><span class="n">unfold</span><span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">kernel_size</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">dilation</span><span class="p">,</span>
                        <span class="bp">self</span><span class="o">.</span><span class="n">padding</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">stride</span><span class="p">)</span>

    <span class="k">def</span> <span class="nf">extra_repr</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="s1">&#39;kernel_size=</span><span class="si">{kernel_size}</span><span class="s1">, dilation=</span><span class="si">{dilation}</span><span class="s1">, padding=</span><span class="si">{padding}</span><span class="s1">,&#39;</span> \
            <span class="s1">&#39; stride=</span><span class="si">{stride}</span><span class="s1">&#39;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="o">**</span><span class="bp">self</span><span class="o">.</span><span class="vm">__dict__</span><span class="p">)</span></div>
</pre></div>

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